The invention relates to an aid for teaching the basic concepts of arithmetic. In view of its purpose, this teaching aid is suited primarily for teaching in elementary schools.
In the lowest school levels, in which the pupils are taught the basic concepts of arithmetic, teachers repeatedly experience that the greatest difficulty is in teaching the less gifted pupils the quantity concept which lies hidden in each number. Such pupils only appear to learn the basic concepts, because they acquire the habit of learning by memory the numerical values, or results. The quantity concept is nevertheless entirely absent for them, which is demonstrated by their inability to carry out arithmetic operations with unfamiliar numerical values, because they have not yet memorized these.
Aids for teaching the basic concepts of arithmetic have been known for a long time. The most familiar of these is the abacus. Yet, this clearly can be used only for addition and subtraction. Multiplication and division require a certain quantity concept, or an abstraction, for the balls of the abacus are not identified naturally by numbers. The pupil sees the many balls, but must first count them. In this he can see the quantity itself, but not the particular number which is associated with that quantity. The abacus uses primarily the quantity concept, and to a lesser degree the numerical concept associated with it.
Also known are learning toys. In principle, these have two levers. One end of each is movable along a scale. The other end of each is connected together and to a pointer mechanism. The individual adjustment of both levers along the scale results in a repositioning and pivoting of the pointer, which moves over an interchangeable plate. The plate is provided with numerical values positioned so that the pointer always indicates the numerical result which follows from operating on the chosen numerical values of the scale with the chosen operator. For example, if both the levers are set on the scale to the values 3 and 6, then the pointer will take a particular position. On an addition plate it will indicate the value 9, and on a multiplication plate the value 18. Here the numerical concept is relatively clear. However, because of the relatively complicated movement and pivoting of the pointer, the numbers on the two plates must be placed in an unfamiliar order, the logic of which is at first not entirely clear, even to adults. For the children there does not seem to be any relationship between the numerical result of the arithmetic operation and the other numbers. This difficulty is augmented by the appearance on the multiplication plate of only those values which result from multiplying by a whole unit, a number less than ten. Intervening numbers are left out for reasons of space, which makes it more difficult for pupils to grasp numerical concept for the particular setting. In this way, the pupils are given essentially only an abstract numerical concept, and not the quantitative concept associated with it.
An object of the invention is to provide a handy, readily portable teaching aid for learning the basic concepts of arithmetic which in a clear way associates the numerical values with the corresponding quantitative concept, which without interchangeable parts also introduces the four basic concepts of arithmetic (addition, subtraction, multiplication, and division), and which gives the results of the particular operation to the pupil in an elementary logical arrangement with respect to the other numerical values which is natural and readily grasped by the pupil.